MCMCpoissonChangepoint       package:MCMCpack       R Documentation

_M_a_r_k_o_v _C_h_a_i_n _M_o_n_t_e _C_a_r_l_o _f_o_r _a _P_o_i_s_s_o_n _M_u_l_t_i_p_l_e _C_h_a_n_g_e_p_o_i_n_t _M_o_d_e_l

_D_e_s_c_r_i_p_t_i_o_n:

     This function generates a sample from the posterior distribution
     of a Poisson model with multiple changepoints. The function uses
     the Markov chain Monte Carlo method of Chib (1998). The user
     supplies data and priors, and a sample from the posterior
     distribution is returned as an mcmc object, which can be
     subsequently analyzed with functions provided in the coda package.

_U_s_a_g_e:

     MCMCpoissonChangepoint(data,  m = 1, c0 = NA, d0 = NA, a = NULL, b = NULL,
                 burnin = 10000, mcmc = 10000, thin = 1, verbose = 0, seed = NA,
                 lambda.start = NA, P.start = NA,
                 marginal.likelihood = c("none", "Chib95"), ...)  

_A_r_g_u_m_e_n_t_s:

    data: The data.

       m: The number of changepoints.

      c0: c0 is the shape parameter for Gamma prior on lambda (the
          mean). No default value is provided.

      d0: d0 is the scale parameter for Gamma prior on lambda (the
          mean). No default value is provided.

       a: a is the shape1 beta prior for transition probabilities. By
          default, the expected duration is computed and corresponding
          a and b values are assigned. The expected duration is the
          sample period divided by the number of states.

       b: b is the shape2 beta prior for transition probabilities. By
          default, the expected duration is computed and corresponding
          a and b values are assigned. The expected duration is the
          sample period divided by the number of states.

  burnin: The number of burn-in iterations for the sampler.

    mcmc: The number of MCMC iterations after burn-in.

    thin: The thinning interval used in the simulation.  The number of
          MCMC iterations must be divisible by this value.

 verbose: A switch which determines whether or not the progress of the
          sampler is printed to the screen.  If 'verbose' is greater
          than 0, the iteration number and the posterior density
          samples are printed to the screen every 'verbose'th
          iteration.

    seed: The seed for the random number generator.  If NA, current R
          system seed is used.

lambda.start: The starting values for the lambda vector. This can
          either be a scalar or a column vector with dimension equal to
          the number of lambdas. The default value of NA will use draws
          from the Uniform distribution with the same boundary with the
          data as the starting value. If this is a scalar, that value
          will serve as the starting value mean for all of the lambdas.

 P.start: The starting values for the transition matrix. A user should
          provide a square matrix with dimension equal to the number of
          states. By default, draws from the 'Beta(0.9, 0.1)' are used
          to construct a proper transition matrix for each raw except
          the last raw.

marginal.likelihood: How should the marginal likelihood be calculated?
          Options are: 'none' in which case the marginal likelihood
          will not be calculated, and 'Chib95' in which case the method
          of Chib (1995) is used.

     ...: further arguments to be passed

_D_e_t_a_i_l_s:

     'MCMCpoissonChangepoint' simulates from the posterior distribution
     of a Poisson model with multiple changepoints.

     The model takes the following form:

                Y_t ~ Poisson(lambda_i), i = 1,...,k.

     Where k is the number of states.

     We assume Gamma priors for lambda_i and Beta priors for transition
     probabilities:

                       lambda_i ~ Gamma(c0, d0)


                   p_ii ~ Beta(a, b), i = 1,...,k.

     Where k is the number of states.

     The simulation is done in compiled C++ code to maximize
     efficiency.

_V_a_l_u_e:

     An mcmc object that contains the posterior sample. This object can
     be summarized by functions provided by the coda package. The
     object contains an attribute 'prob.state' storage matrix that
     contains the probability of state_i for each period, and the
     log-marginal likelihood of the model ('logmarglike').

_A_u_t_h_o_r(_s):

     Jong Hee Park, jhp@uchicago.edu, <URL:
     http://home.uchicago.edu/~jhp/>.

_R_e_f_e_r_e_n_c_e_s:

     Siddhartha Chib. 1995. "Marginal Likelihood from the Gibbs
     Output." _Journal of the American Statistical Association_. 90:
     1313-1321.

     Siddhartha Chib. 1998. "Estimation and comparison of multiple
     change-point models." _Journal of Econometrics_. 86: 221-241.

_S_e_e _A_l_s_o:

     'plotState', 'plotChangepoint'

_E_x_a_m_p_l_e_s:

         ## Not run: 
         set.seed(1973)
         n           <-  100
         true.lambda <-  c(5, 8)
         y1          <-  rpois(n/2, true.lambda[1])
         y2          <-  rpois(n/2, true.lambda[2])
         y           <-  c(y1, y2)

         model1 <-  MCMCpoissonChangepoint(y, m=1, c0=6.85, d0=1, verbose = 10000, marginal.likelihood = "Chib95")
         model2 <-  MCMCpoissonChangepoint(y, m=2, c0=6.85, d0=1, verbose = 10000, marginal.likelihood = "Chib95")
         model3 <-  MCMCpoissonChangepoint(y, m=3, c0=6.85, d0=1, verbose = 10000, marginal.likelihood = "Chib95")
         model4 <-  MCMCpoissonChangepoint(y, m=4, c0=6.85, d0=1, verbose = 10000, marginal.likelihood = "Chib95")
         model5 <-  MCMCpoissonChangepoint(y, m=5, c0=6.85, d0=1, verbose = 10000, marginal.likelihood = "Chib95")

         print(BayesFactor(model1, model2, model3, model4, model5))

         ## Draw plots using the "right" model
         plotState(model1)
         plotChangepoint(model1)
         ## End(Not run)

